C + KNO2 = CO2 + N2 + K2CO3

C activated charcoal + KNO_2 potassium nitrite ⟶ CO_2 carbon dioxide + N_2 nitrogen + K_2CO_3 pearl ash

Balance the chemical equation algebraically: C + KNO_2 ⟶ CO_2 + N_2 + K_2CO_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 C + c_2 KNO_2 ⟶ c_3 CO_2 + c_4 N_2 + c_5 K_2CO_3 Set the number of atoms in the reactants equal to the number of atoms in the products for C, K, N and O: C: | c_1 = c_3 + c_5 K: | c_2 = 2 c_5 N: | c_2 = 2 c_4 O: | 2 c_2 = 2 c_3 + 3 c_5 Since the coefficients are relative quantities and underdetermined, choose a coefficient to set arbitrarily. To keep the coefficients small, the arbitrary value is ordinarily one. For instance, set c_3 = 1 and solve the system of equations for the remaining coefficients: c_1 = 3 c_2 = 4 c_3 = 1 c_4 = 2 c_5 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 3 C + 4 KNO_2 ⟶ CO_2 + 2 N_2 + 2 K_2CO_3

+ ⟶ + +

activated charcoal + potassium nitrite ⟶ carbon dioxide + nitrogen + pearl ash

Construct the equilibrium constant, K, expression for: C + KNO_2 ⟶ CO_2 + N_2 + K_2CO_3 Plan: • Balance the chemical equation. • Determine the stoichiometric numbers. • Assemble the activity expression for each chemical species. • Use the activity expressions to build the equilibrium constant expression. Write the balanced chemical equation: 3 C + 4 KNO_2 ⟶ CO_2 + 2 N_2 + 2 K_2CO_3 Assign stoichiometric numbers, ν_i, using the stoichiometric coefficients, c_i, from the balanced chemical equation in the following manner: ν_i = -c_i for reactants and ν_i = c_i for products: chemical species | c_i | ν_i C | 3 | -3 KNO_2 | 4 | -4 CO_2 | 1 | 1 N_2 | 2 | 2 K_2CO_3 | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression C | 3 | -3 | ([C])^(-3) KNO_2 | 4 | -4 | ([KNO2])^(-4) CO_2 | 1 | 1 | [CO2] N_2 | 2 | 2 | ([N2])^2 K_2CO_3 | 2 | 2 | ([K2CO3])^2 The equilibrium constant symbol in the concentration basis is: K_c Mulitply the activity expressions to arrive at the K_c expression: Answer: | | K_c = ([C])^(-3) ([KNO2])^(-4) [CO2] ([N2])^2 ([K2CO3])^2 = ([CO2] ([N2])^2 ([K2CO3])^2)/(([C])^3 ([KNO2])^4)

Construct the rate of reaction expression for: C + KNO_2 ⟶ CO_2 + N_2 + K_2CO_3 Plan: • Balance the chemical equation. • Determine the stoichiometric numbers. • Assemble the rate term for each chemical species. • Write the rate of reaction expression. Write the balanced chemical equation: 3 C + 4 KNO_2 ⟶ CO_2 + 2 N_2 + 2 K_2CO_3 Assign stoichiometric numbers, ν_i, using the stoichiometric coefficients, c_i, from the balanced chemical equation in the following manner: ν_i = -c_i for reactants and ν_i = c_i for products: chemical species | c_i | ν_i C | 3 | -3 KNO_2 | 4 | -4 CO_2 | 1 | 1 N_2 | 2 | 2 K_2CO_3 | 2 | 2 The rate term for each chemical species, B_i, is 1/ν_i(Δ[B_i])/(Δt) where [B_i] is the amount concentration and t is time: chemical species | c_i | ν_i | rate term C | 3 | -3 | -1/3 (Δ[C])/(Δt) KNO_2 | 4 | -4 | -1/4 (Δ[KNO2])/(Δt) CO_2 | 1 | 1 | (Δ[CO2])/(Δt) N_2 | 2 | 2 | 1/2 (Δ[N2])/(Δt) K_2CO_3 | 2 | 2 | 1/2 (Δ[K2CO3])/(Δt) (for infinitesimal rate of change, replace Δ with d) Set the rate terms equal to each other to arrive at the rate expression: Answer: | | rate = -1/3 (Δ[C])/(Δt) = -1/4 (Δ[KNO2])/(Δt) = (Δ[CO2])/(Δt) = 1/2 (Δ[N2])/(Δt) = 1/2 (Δ[K2CO3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| activated charcoal | potassium nitrite | carbon dioxide | nitrogen | pearl ash formula | C | KNO_2 | CO_2 | N_2 | K_2CO_3 Hill formula | C | KNO_2 | CO_2 | N_2 | CK_2O_3 name | activated charcoal | potassium nitrite | carbon dioxide | nitrogen | pearl ash IUPAC name | carbon | potassium nitrite | carbon dioxide | molecular nitrogen | dipotassium carbonate

| activated charcoal | potassium nitrite | carbon dioxide | nitrogen | pearl ash molar mass | 12.011 g/mol | 85.103 g/mol | 44.009 g/mol | 28.014 g/mol | 138.2 g/mol phase | solid (at STP) | solid (at STP) | gas (at STP) | gas (at STP) | solid (at STP) melting point | 3550 °C | 350 °C | -56.56 °C (at triple point) | -210 °C | 891 °C boiling point | 4027 °C | | -78.5 °C (at sublimation point) | -195.79 °C | density | 2.26 g/cm^3 | 1.915 g/cm^3 | 0.00184212 g/cm^3 (at 20 °C) | 0.001251 g/cm^3 (at 0 °C) | 2.43 g/cm^3 solubility in water | insoluble | | | insoluble | soluble surface tension | | | | 0.0066 N/m | dynamic viscosity | | | 1.491×10^-5 Pa s (at 25 °C) | 1.78×10^-5 Pa s (at 25 °C) | odor | | | odorless | odorless |